The present invention is directed to electro-optical tracking systems, and particularly airborne systems requiring stabilization. In such systems the optical sensor or mirror focused on the optical sensor is mounted on a gimbal which permits tracking along the desired line-of-sight to a target. The system must permit the sensor to track along the line-of-sight despite motions of the aircraft. Such an aircraft-mounted electro-optical system is termed a heliostat and provides a space stabilized look direction from the aircraft.
A prior art stabilization system for maintaining a fixed line-of-sight of an optical instrument on an aircraft is described in U.S. Pat. No. 3,518,016. Such system comprises a line-of-sight mirror mounted on a gimbal, with servo motors for rotating the mirror about the gimbal axis, and wherein gyros sense motion about the gimbal axis to generate feedback control signals which are applied to torque motors for controlling mirror rotation.
In another such gimbaled tracking system seen in U.S. Pat. No. 4,021,716, the angular velocities of the rotating members are sensed to provide a feedback signal for providing torque compensation, which includes bearing friction torque compensation.
The line-of-sight stabilization error of an airborne pointing and tracking system caused by response to gimbal bearing friction torque is often of sufficient magnitude to be the object of an intense design effort. Similarly, friction can limit the smoothness of robot motion trajectories. In the airborne tracking system, this torque impinges on the stabilized member of the system's gimbal as a function of relative angular motion between that element and the gimbal's base (i.e., the aircraft). It is counteracted in conventional systems by the torque motor of a stabilization feedback loop. An inertial sensor (a gyro, for example) mounted on the stabilized member is used as the feedback element. The loop functions to produce corrective motor torque in proportion to error measured by the feedback sensor. The constant of proportionality associated with this feedback process is often referred to as the stabilization stiffness and may be functionally thought of as a spring which connects the stabilized member to, and attempts to fix it in, inertial space.
While conventional feedback operation greatly reduces friction-related errors, it is often by an insufficient amount. Minimum bearing friction levels are often fixed by system weight, geometry, and vibration environment. Maximum stabilization stiffnesses are likewise limited by loop stability considerations, sensor noise, gimbal size and structural resonances. Taken together, then, the ratio of friction torque to stiffness often yields stabilization errors which are unacceptably large given the required compatibility with other system constraints.
A solution to these conflicting requirements is possible if friction torque can be accurately predicted in real-time. A counteracting command can then be applied to the stabilization subsystem which negates the friction torque before its effect is measured by the feedback sensor. Now, instead of being proportional to full friction levels, stabilization error is proportional to the much smaller mismatch between actual friction torque and that predicted by the model.
The detailed knowledge of friction behavior necessary to achieve accurate real-time modeling has, however, previously been lacking. This is particularly true concerning the transient behavior of friction caused by relative motion polarity reversals of the system's gimbal members, a particular problem in airborne stabilization systems where reversals occur quite frequently in response to aircraft motions.
Conventional analysis of this bearing friction has not proven satisfactory. Such analysis had suggested that the transition time in going from opposite polarity, fixed values of rolling friction is inversely related, in a non-linear manner to the magnitude of relative bearing motion.
FIG. 2 of the drawings is a plot illustrating the friction torque waveform versus time based on experimental observations. This plot shows a transition time .tau., from one rolling friction torque value +T.sub.c to the other -T.sub.c.
It has been determined that the optimum time constant associated with the transition time for minimized motion of the stable element as seen in FIG. 2 is actually strongly correlated with the magnitude of relative bearing acceleration, and can be closely approximated to ##EQU1## where .tau..sub.OPT is the optimum exponential time constant and .lambda..sub.RMS is the root mean square relative bearing angular acceleration in deg/sec/sec. The value 0.37 is a representative value had from a specific system that was analyzed and has to be determined for each specific system.